Pretend the hot brick extracts heat from the cold brick and becomes hotter. Would this violate the Law of Conservation of Energy?
No, the process you described would not violate the Law of Conservation of Energy. The Law of Conservation of Energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another.
In the scenario you described, the hot brick extracting heat from the cold brick is a transfer of thermal energy from a region of higher temperature (hot brick) to a region of lower temperature (cold brick). This transfer of energy does not violate the law because the total amount of energy in the system remains the same. The energy lost by the hot brick is gained by the cold brick, resulting in an overall energy balance.
To calculate the energy transfer between the bricks, you can use equations from thermodynamics, such as Fourier's Law of Heat Conduction or the heat transfer equation. These equations take into account factors like the temperature difference between the bricks, the thermal conductivity of the materials, and the surface area in contact.
Understanding and applying the principles of heat transfer and energy conservation are essential to explain and analyze such situations properly.